Delta function Definition and 366 Threads

i can't solve there problem, please help me 1) delta(y^2-a^2) = 1/absolute 2a[delta(y-a)+delta(y+a)] 2) f(y)delta(y-a) = f(a)delta(y-a)

I am sort of stuck on this one: compute Laplace trasnform of this signal (directly by evaluating the integral) f(t) = cos(pi*t + theta)*delta(t-2); I know what the LT integral looks like, but I don't think I'm evaluating it right. Would the answer be just: cos(pi*t + theta)*e^(-2s) ...

NOTE: I actually found the correct answer while I was typing this :rolleyes: and since I already had it typed, I figured i would post anyway. mods you can do with it as you please or leave it for reference. thanks Here's the problem: A uniform beam of length L carries a concentrated...

Can anyone tell me the difference between the Delta function and the Kronecker delta? It seems that both are 1 at a certain point and 0 otherwise... The delta function is a eigenfunction of x and the Kronecker delta is ... i'm kind of confused..

1. INTRODUCTION Many students become frustrated when they first meet the Dirac Delta function, typically in a course involving electrostatics, or Laplace transforms. As it is commonly presented, the Dirac function seems totally meaningless: Either, it is "defined" as...

Can someone help me prove the following: L=\mathop \lim\limits_{k\to \infty}\int_{-\frac{3}{4k}}^{\frac{3}{4k}} f(x)[-\frac{16k^3}{9}x^2+k]dx=f(0) I'm pretty sure at the limit, -\frac{16k^3}{9}x^2+k becomes a delta function. Essentially, it's that section of a narow parabola above...

I have a test in Diff Eq. tommorow and part of the test is inovling the Dirac Delta function. I have no clue as to what it is at all. More specifically its Laplace and Inverse Laplace. If anyone could explain to me what the delta function is and how to use in in diff eq and what are its...

Can someone explain me the Dirac Delta function for the function: \vec A = \frac{\hat r}{r^2}

Hello, I'm having trouble with the following problem: The spherically symmetrical electrostatic potential of a particular object is given (in spherical coordinates) by: V(\vec{r})=V(r)=c\frac{exp{(\frac{-2r}{a})}}{4\pi\varepsilon r} (1+\frac{r}{a}) I found the electrostatic field in...

let S be the Unit Step function for a function with a finite jump at t0 we have: (*) L{F'(t)}=s f(s)-F(0)-[F(t0+0)-F(t0-0)]*exp(-s t0)] so: L{S'(t-k)}=s exp(-s k)/s-0-[1-0]*exp(-s k) = 0 & k>0 but S'(t-k)=deltadirac(t-k) and we know that L{deltadirac(t-k)}=exp(-s k) so...

So I read that the delta function potential well has one and only one bound state. This seems to give a precise momentum and position as the bound state has a definite energy and the particle must be in the well. This seems to be a violation of the HUP. Is the physical impossibility of...

Okay...so here's the thing. I have been researching the dirac Delta properties. The sights I've visited, thus far, are moderately helpful. I'm looking to tackle this question I'm about to propose, so for you Brains out there (the truly remarkable :rolleyes:) please don't post a solution...

I am going again over Polchinski's excercises, trying to work them and using http://schwinger.harvard.edu/~headrick/polchinski.html when I get stuck. In problem 2.1, P. wants us to show that \partial \bar{\partial} ln \vert z \vert^2 = 2 \pi \delta^2(z,\bar{z}) and Headrick, introducing...

in the attatch file there is the dd function. what i want to know is: when x doesn't equal 0 the function equals 0 and the inegral is the integral of the number 0 which is any constant therefore i think the integral should be equal 0. can someone show me how this integral equals 1? for...

I'm not sure what field this fits with, so I'll post here. I was introduced to the delta function in physics class. I understand what it means, but how do you use it?

Supposedly, ∫ ez*(z - z0)f(z) dz*dz is proportional to f(z0) much in the same way that (1/2π)∫ eiy(x - x0)f(x) dxdy = ∫ δ(x - x0)f(x) dx = f(x0) Is this true? Could someone help convince me of it, or point me to a text? I would say that even if true, it...